Clusters of galaxies, which occupy a unique position in hierarchical structure formation, are invaluable cosmological probes and laboratories for astrophysical processes. Cluster scaling relations, which connect their masses and observable properties, provide the link between these two roles. Cosmological constraints derived from cluster abundances often rely on calibrations or functional forms of these relations. On the other hand, the form and evolution of the mass-observable relations are affected by astrophysical processes during
cluster formation. Understanding these processes not only provides insights into cluster physics but also has important implications for cluster cosmology.
In this thesis, we use numerical simulations to study the influence of important physical mechanisms, including gravity, radiative cooling, and heating from active galactic nuclei (AGN), on cluster mass-observable relations. In particular, we investigate the physical origin of the intrinsic scatter around the best-fit relations by correlating it with measures of cluster structure, dynamical state, and AGN activity. Using a cosmological N -body plus
hydrodynamic simulation produced using the FLASH code, we study the impact of cluster structure and dynamical state on the distribution of scatter in the X-ray temperature
and Sunyaev-Zel’dovich (SZ) scaling relations. We also examine possible systematic biases in cluster cosmology, such as sample selection in cluster surveys, assumptions in self-calibration studies, and correlated errors in combining X-ray and SZ mass estimates.
Correctly simulating cluster properties, especially inside cluster cores, requires additional
baryonic physics, including radiative cooling and some heating mechanisms such as AGN feedback. However, because of the extreme dynamic range required to capture the rich physics involved in accretion onto and feedback by the supermassive black holes (SMBH)
in AGN, current modeling of AGN in cosmological simulations is highly phenomenological and relies on heterogeneous parameterizations. We perform a systematic sensitivity study on a variety of these models and parameters and quantify the current theoretical uncertain-
ties in the predicted cluster global quantities. This study is an important step toward the development of more robust AGN models within a cosmological framework.